散开卡片网格的“弧形”

我有n卡数。每张卡的a宽度单位。
许多流行的纸牌游戏在“呈扇形”位置显示一手纸牌（参见下图），我也想这样做。通过使用以下公式，我可以将卡成弧形放置：

// NOTE: UE4 uses a left-handed, Z-up coordinate system.
//  (+X = Forward, +Y = Right, and +Z = Up)

// NOTE: Card meshes have their pivot points in the center of the mesh
//  (meshSize * 0.5f = local origin of mesh)

// n = Number of card meshes
// a = Width of each card mesh

const auto arcWidth = 0.8f;
const auto arcHeight = 0.15f;
const auto rotationAngle = 30.f;
const auto deltaAngle = 180.f;
const auto delta = FMath::DegreesToRadians(deltaAngle) / (float)(n);
const auto halfDelta = delta * 0.5f;
const auto halfMeshWidth = a * 0.5f;
const auto radius = halfMeshWidth + (rotationAngle / FMath::Tan(halfDelta));

for (unsigned y = 0; y < n; y++)
{
    auto ArcX = (radius * arcWidth) * FMath::Cos(((float)y * delta) + halfDelta);
    auto ArcY = (radius * arcHeight) * FMath::Sin(((float)y * delta) + halfDelta);
    auto ArcVector = FVector(0.f, ArcX, ArcY);

    // Draw a line from the world origin to the card origin
    DrawDebugLine(GetWorld(), FVector::ZeroVector, ArcVector, FColor::Magenta, true, -1.f, 0, 2.5f);
}

这是《炉石传说》的5张卡片示例：

这是《杀戮尖塔》的5张卡片示例：

但是我正在产生的结果很好……次优：

No matter how I tweak the variables, the cards on the far left and far right side are getting squashed together into the hand. I imagine this has to do with how the points of a circle are distributed, and then squashed downwards (via arcHeight) to form an ellipse? In any case, you can see that the results are far from similar, even though if you look closely at the example references, you can see that an arc exists from the center of each card (before those cards are rotated in local space).

What can I do to achieve a more evenly spaced arc?